Problem 2 - Algebra A Combined Function

Question

Find each number described. For Exercises 1 and 2 , the solutions have been started for you. What number is \(88 \%\) of \(1000 ?\) Start the solution: UNDERSTAND the problem. Reread it as many times as needed. TRANSLATE into an equation. (Fill in the blanks below.) Finish with: SOLVE and INTERPRET

Step-by-Step Solution

Answer

The number is 880.

Step 1: Understand the Problem

The goal is to find out what number represents 88% of 1000. This means we are looking for a number that is equivalent to 88 percent of 1000.

Step 2: Translate into an Equation

Translate the verbal problem into a mathematical equation. To find 88% of a number, express 88% as a decimal: \(0.88\). Thus, the equation to solve is: \( x = 0.88 \times 1000 \).

Step 3: Solve the Equation

Now, solve the equation \( x = 0.88 \times 1000 \). Calculate the multiplication to find \(x\). This can be done by multiplying 0.88 by 1000.

Step 4: Calculate Multiplication

Perform the multiplication: \(0.88 \times 1000 = 880\). Therefore, the number that is 88% of 1000 is 880.

Step 5: Interpret the Result

Interpretation means understanding the solution. Since 880 is the result, this confirms that 880 is indeed 88% of 1000.

Key Concepts

mathematical equations

Mathematical equations are tools we use to describe relationships between numbers and variables. In the context of percentage problems, equations help us to simplify the task of finding specific percentages of numbers. In the exercise, "What number is 88% of 1000?", we're using an equation to express this relationship and find the answer. The equation derived here is: \( x = 0.88 \times 1000 \). The \(0.88\) represents the 88% as a decimal, and the multiplication finds what portion of 1000 equals 88%. By using equations, you can solve various problems that involve percentages, ratios, or rates by setting up a clear mathematical relationship.

Equations help us quantify abstract relationships in a way that's easy to calculate, leading to precise results. They form a framework where we can input values and directly find the answer, making them critical for problems in algebra and beyond. Understanding how to translate word problems into equations is key for success in math.

understanding word problems

Understanding word problems is essential for solving them correctly. It might seem complex when a problem is described with words, but breaking it down can simplify it. The first step is to carefully read the problem, identifying what is being asked and the information given.

For instance, in our exercise, the problem states: "What number is 88% of 1000?" Here, we need to recognize:

• The percentage given: 88%
• The whole value: 1000
• The task: find 88% of that whole

By focusing on these keywords, we can transfer our understanding into mathematical expressions. Confer back to basic concepts like percentages, which are just parts of a whole, represented sometimes as decimals or fractions. In this case, converting 88% to a decimal (0.88) is crucial. This understanding allows us to set up the equation needed to find the solution.

Thus, dissecting word problems involves recognizing key components and translating them into mathematical terms. Practice enhances this skill, allowing quicker recognition and easier problem-solving.

step-by-step problem solving

Step-by-step problem solving is a methodical approach to tackle problems with clarity and precision. It assures that each stage of a problem is well understood before moving on to the next. For our percentage problem, the solution involves several clear steps:

1. **Understand the Problem:**
Determine what the problem is asking. We need to find what number 88% of 1000 represents.

2. **Translate into an Equation:**
Convert the word problem into a mathematical equation: \( x = 0.88 \times 1000 \). Express 88% as the decimal 0.88 for easy calculation.

3. **Solve the Equation:**
Perform the arithmetic to find \( x \). Here, it's multiplying 0.88 by 1000.

4. **Calculate Multiplication:**
The actual multiplication gives you \( 0.88 \times 1000 = 880 \).

5. **Interpret the Result:**
Finally, interpret what 880 represents – confirming it as 88% of 1000.

This structured approach ensures no steps are missed and helps to break down complex problems into manageable parts. Practicing this approach builds confidence and skills to solve more complex equations and word problems efficiently.